A Display generally consists of an array of pixels (picture elements) where one pixel represents a dot on the screen. This dot could be just white or black or may be represented with varying shades of gray (grayscale). A pixel could also represent multi-color where the individual colors are called sub-pixels since it takes all of them merged together to define the pixel color. Color displays typically have 3 subpixels, Red, Green, and Blue since these can be manipulated in combination to produce all of the needed colors. An integrated display may have a memory map where a memory address contains the data for one pixel on the screen. The computer writes to the memory location and hardware translates that memory data to the displayed pixel.
The Display on a mobile device is generally built into the device itself unlike a desktop computer where the display (usually called a monitor) is a separate device connected via a cable to the computer hardware. Most modern displays are bit (pixel) addressable which means that the software can control the display at the individual pixel level. This is normally done with an X/Y grid to form the address of the pixel. Thus a pixel can be identified as being in a certain row and a certain column of the display grid.
Characters and images are created by highlighting the appropriate pixels to form the shape desired. Early in computer technology the display was not bit addressable but rather a fixed set of character positions were used on the screen and the software defined the character for a particular character position and hardware then translated this to the bit image on the screen.
 Screen Size
The screen size is generally talked about two different ways. There is the actual screen dimensions for the display and there is the number of pixels used to define the screen area such as 800x600 which means that the longer side has 800 pixels and the shorter side has is 600 pixels wide. The total number of pixels in this screen is thus 480,000.
 Physical size
The physical size is often quoted as a single number which is the measure of the diagonal dimension of the display. This can be stated in inches or cm (or mm). With a given aspect ratio (ratio of width to length) the actual size can be determined. For example a standard TV has an aspect ratio of 4:3 which means a 5" display is really 4 inches wide and 3 inches tall. The newest TVs are now called wide-screen with an aspect ratio of 16:9. A 5" wide-screen display would actually have less area than a screen with a display that was closer to square. For reading purposes the area of the screen is a better judge. For 4:3 this would be 12 square inches by 16:9 would be closer to 11.
Mobile Devices can have any aspect ratio from 1:1 to very narrow. There is no standard but, for reading, 4:3, 3:2, 16:9 are popular ratios.
 Screen resolution
The ratio of the number of pixels to the screen size can be used to specify the resolution of the display. This is normally specified a PPI (pixels per inch) The For example 600 pixels on a 3" wide display would be 200 ppi. This is similar to a printer with a 200 dpi output. DPI (dots per inch) and PPI are the same for monochrome systems but different for Color. For a Reading device 100 ppi or more is considered OK however some people are bothered by a ppi this small. A ppi of 150 or more is generally satisfactory. Small screens are often held closer to your eyes and would therefore need to have a higher ppi. Apple offers very high resolution that they call a Retina display. Generally Computer screens are less than 100 ppi and a TV about 50 ppi.
A color pixel is generally made up of 3 dots: 1 red, 1 green, and 1 blue. These are called sub-pixels. Each sub-pixel is a dot so dpi would be higher than ppi. One trick to improve the apparent resolution of a color display to to smooth the edges by using an adjacent sub-pixel. The eye cannot really see color in an image if it is very small so turning on just one sub-pixel which will only show as gray but the smoothness will be apparent. Microsoft uses this technique to achieve better apparent resolution with "cleartype" reading software. The improvement in apparent resolution can be as much as 50%. If the fonts are designed correctly they will look very good on any of the eBook Reading devices. Really tiny fonts or accent marks could look poor on low resolution devices.
For video use a lower ppi is fine. The motion and short time for each image will make the image seem clearer.
It is possible that the horizontal and vertical resolution are not the same. In this case the pixel would not be square. The page on screen sizes has comparisons for different screens.
 Display refresh
Many displays require a refresh. This is because once the display image is sent to the screen it will begin to fade away. The length of time the display will remain on the screen is called its persistence. The method used to keep the display on the screen is to refresh it often. If it is refreshed often enough the user will perceive the data never faded at all. Refresh times are generally 60 times per second or more. Low refresh times can cause the image to flicker which will cause eye fatigue when reading on the unit.
Typically refresh is done from a hardware controller that works out of a portion of RAM memory dedicated to the display. The software in the system writes the data to this memory location and it will then be displayed on the screen automatically. The memory is typically a bitmapped image of what the screen will show. It some cases there may be multiple bitmapped images where the software constructs the new page behind the scenes and then the display controller switches to the new memory map and shows the new data instantly.
Some display technologies, most notably e-paper and LCD, do not require refreshing. LCD require power to retain it screen contents. E-paper does not need power to the screen but will lose a little of its contrast after a while. Even screens without refresh will typically have a RAM based memory area to stage the image.